ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 25 Sep 2023 09:22:52 GMT2023-09-25T09:22:52Z501681- Counting functions and expected values for the lattice profile at nhttps://scholarbank.nus.edu.sg/handle/10635/129719Title: Counting functions and expected values for the lattice profile at n
Authors: Dorfer, G.; Meidl, W.; Winterhof, A.
Abstract: Recently, Dorfer and Winterhof introduced and analyzed a lattice test for sequences of length n over a finite field. We determine the number of sequences η of length n with given largest dimension Sn(η)=S for passing this test. From this result we derive an exact formula for the expected value of Sn(η). For the binary case we characterize the (infinite) sequences η with maximal possible Sn(η) for all n. © 2004 Elsevier Inc. All rights reserved.
Fri, 01 Oct 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1297192004-10-01T00:00:00Z
- Exponential approximation for the nearly critical Galton-Watson process and occupation times of Markov chainshttps://scholarbank.nus.edu.sg/handle/10635/105145Title: Exponential approximation for the nearly critical Galton-Watson process and occupation times of Markov chains
Authors: Peköz, E.A.; Röllin, A.
Abstract: In this article we provide new applications for exponential approximation using the framework of Peköz and Röllin (2011), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new exponential approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erdo{double acute}s-Taylor theorem.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051452011-01-01T00:00:00Z
- Exponential approximation by stein's method and spectral graph theoryhttps://scholarbank.nus.edu.sg/handle/10635/105144Title: Exponential approximation by stein's method and spectral graph theory
Authors: Chatterjee, S.; Fulman, J.; Röllin, A.
Abstract: General Berry-Esséen bounds are developed for the exponential distribution using Stein's method and a new concentration inequality approach. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Johnson graph has an exponential limit.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1051442011-01-01T00:00:00Z
- High-quality curvelet-based motion deblurring from an image pairhttps://scholarbank.nus.edu.sg/handle/10635/115434Title: High-quality curvelet-based motion deblurring from an image pair
Authors: Cai, J.-F.; Ji, H.; Liu, C.; Shen, Z.
Abstract: One promising approach to remove motion deblurring is to recover one clear image using an image pair. Existing dual-image methods require an accurate image alignment between the image pair, which could be very challenging even with the help of user interactions. Based on the observation that typical motion-blur kernels will have an extremely sparse representation in the redundant curvelet system, we propose a new minimization model to recover a clear image from the blurred image pair by enhancing the sparsity of blur kernels in the curvelet system. The sparsity prior on the motion-blur kernels improves the robustness of our algorithm to image alignment errors and image formation noise. Also, a numerical method is presented to efficiently solve the resulted minimization problem. The experiments showed that our proposed algorithm is capable of accurately estimating the blur kernels of complex camera motions with low requirement on the accuracy of image alignment, which in turn led to a high-quality recovered image from the blurred image pair. ©2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1154342009-01-01T00:00:00Z
- Adaptive low rank and sparse decomposition of video using compressive sensinghttps://scholarbank.nus.edu.sg/handle/10635/125023Title: Adaptive low rank and sparse decomposition of video using compressive sensing
Authors: Yang, F.; Jiang, H.; Shen, Z.; Deng, W.; Metaxas, D.
Abstract: We address the problem of reconstructing and analyzing surveillance videos using compressive sensing. We develop a new method that performs video reconstruction by low rank and sparse decomposition adaptively. Background subtraction becomes part of the reconstruction. In our method, a background model is used in which the background is learned adaptively as the compressive measurements are processed. The adaptive method has low latency, and is more robust than previous methods. We will present experimental results to demonstrate the advantages of the proposed method. © 2013 IEEE.
Tue, 01 Jan 2013 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1250232013-01-01T00:00:00Z
- Wavelet based restoration of images with missing or damaged pixelshttps://scholarbank.nus.edu.sg/handle/10635/115355Title: Wavelet based restoration of images with missing or damaged pixels
Authors: Ji, H.; Shen, Z.; Xu, Y.
Abstract: This paper addresses the problem of how to restore degraded images where the pixels have been partly lost during transmission or damaged by impulsive noise. A wide range of image restoration tasks is covered in the mathematical model considered in this paper-e.g. image deblurring, image inpainting and super-resolution imaging. Based on the assumption that natural images are likely to have a sparse representation in a wavelet tight frame domain, we propose a regularization-based approach to recover degraded images, by enforcing the analysis-based sparsity prior of images in a tight frame domain. The resulting minimization problem can be solved efficiently by the split Bregman method. Numerical experiments on various image restoration tasks-simultaneously image deblurring and inpainting, super-resolution imaging and image deblurring under impulsive noise-demonstrated the effectiveness of our proposed algorithm. It proved robust to mis-detection errors of missing or damaged pixels, and compared favorably to existing algorithms. © 2011 Global-Science Press.
Sun, 01 May 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1153552011-05-01T00:00:00Z
- Random subgraph counts and u-statistics: Multivariate normal approximation via exchangeable pairs and embeddinghttps://scholarbank.nus.edu.sg/handle/10635/105319Title: Random subgraph counts and u-statistics: Multivariate normal approximation via exchangeable pairs and embedding
Authors: Reinert, G.; Röllin, A.
Abstract: In Reinert and Röllin (2009) a new approach-called the 'embedding method'-was introduced, which allows us to make use of exchangeable pairs for normal and multivariate normal approximations with Stein's method in cases where the corresponding couplings do not satisfy a certain linearity condition. The key idea is to embed the problem into a higher-dimensional space in such a way that the linearity condition is then satisfied. Here we apply the embedding to U-statistics as well as to subgraph counts in random graphs. © Applied Probability Trust 2010.
Tue, 01 Jun 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1053192010-06-01T00:00:00Z
- Blind motion deblurring from a single image using sparse approximationhttps://scholarbank.nus.edu.sg/handle/10635/116051Title: Blind motion deblurring from a single image using sparse approximation
Authors: Cai, J.-F.; Ji, H.; Liu, C.; Shen, Z.
Abstract: Restoring a clear image from a single motion-blurred image due to camera shake has long been a challenging problem in digital imaging. Existing blind deblurring techniques either only remove simple motion blurring, or need user interactions to work on more complex cases. In this paper, we present an approach to remove motion blurring from a single image by formulating the blind blurring as a new joint optimization problem, which simultaneously maximizes the sparsity of the blur kernel and the sparsity of the clear image under certain suitable redundant tight frame systems (curvelet system for kernels and framelet system for images). Without requiring any prior information of the blur kernel as the input, our proposed approach is able to recover high-quality images from given blurred images. Furthermore, the new sparsity constraints under tight frame systems enable the application of a fast algorithm called linearized Bregman iteration to efficiently solve the proposed minimization problem. The experiments on both simulated images and real images showed that our algorithm can effectively removing complex motion blurring from nature images. © 2009 IEEE.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1160512009-01-01T00:00:00Z
- Convergence of cascade algorithms associated with nonhomogeneous refinement equationshttps://scholarbank.nus.edu.sg/handle/10635/103070Title: Convergence of cascade algorithms associated with nonhomogeneous refinement equations
Authors: Jia, R.-Q.; Jiang, Q.; Shen, Z.
Abstract: This paper is devoted to a study of multivariate nonhomogeneous refinement equations of the form φ(x) = g(x) + ∑αεℤs α(α)φ(Mx - α), x ε ℝs, where φ = (φ1,. . . , φr)T is the unknown, g = (g1,. . . , gr)T is a given vector of functions on ℝs, M is an s × s dilation matrix, and a is a finitely supported refinement mask such that each α(α) is an r × r (complex) matrix. Let φ0 be an initial vector in (L2(ℝs))r. The corresponding cascade algorithm is given by φk= φ + ∑αεℤs α(α)φk-1(M · - α), k = 1,2, . . . . In this paper we give a complete characterization for the L2-convergence of the cascade algorithm in terms of the refinement mask a, the nonhomogeneous term g, and the initial vector of functions φ0. © 2000 American Mathematical Society.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030702001-01-01T00:00:00Z
- Compactly supported (bi)orthogonal wavelets generated by interpolatory refinable functionshttps://scholarbank.nus.edu.sg/handle/10635/103005Title: Compactly supported (bi)orthogonal wavelets generated by interpolatory refinable functions
Authors: Ji, H.; Shen, Z.
Abstract: This paper provides several constructions of compactly supported wavelets generated by interpolatory refinable functions. It was shown in [7] that there is no real compactly supported orthonormal symmetric dyadic refinable function, except the trivial case; and also shown in [10, 18] that there is no compactly supported interpolatory orthonormal dyadic refinable function. Hence, for the dyadic dilation case, compactly supported wavelets generated by interpolatory refinable functions have to be biorthogonal wavelets. The key step to construct the biorthogonal wavelets is to construct a compactly supported dual function for a given interpolatory refinable function. We provide two explicit iterative constructions of such dual functions with desired regularity. When the dilation factors are larger than 3, we provide several examples of compactly supported interpolatory orthonormal symmetric refinable functions from a general method. This leads to several examples of orthogonal symmetric (anti-symmetric) wavelets generated by interpolatory refinable functions.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030051999-01-01T00:00:00Z
- Compactly supported tight affine spline frames in L2 (ℝd)https://scholarbank.nus.edu.sg/handle/10635/103010Title: Compactly supported tight affine spline frames in L2 (ℝd)
Authors: Amos, R.; Shen, Z.
Abstract: The theory of fiberization is applied to yield compactly supported tight affine frames (wavelets) in L2(ℝd) from box splines. The wavelets obtained are smooth piecewise-polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of "mother wavelets", however, increases with the increase of the required smoothness. Two bivariate constructions, of potential practical value, art highlighted. In both, the wavelets are derived from four-direction mesh box splines that are refinable with respect to the dilation matrix (1 1 1 -1).
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030101998-01-01T00:00:00Z
- Construction of schauder decomposition on banach spaces of periodic functionshttps://scholarbank.nus.edu.sg/handle/10635/103054Title: Construction of schauder decomposition on banach spaces of periodic functions
Authors: Goh, S.S.; Lee, S.L.; Shen, Z.; Tang, W.S.
Abstract: This paper deals with Schauder decompositions of Banach spaces X2x of 2π-periodic functions by projection operators Pk onto the subspaces Vk, k = 0,1,..., which form a multiresolution of X2x. The results unify the study of wavelet decompositions by orthogonal projections in the Hilbert space L2x 2 on one hand and by interpolatory projections in the Banach space C2x on the other. The approach, using "orthogonal splines", is constructive and leads to the construction of a Schauder decomposition of X2x and a biorthogonal system for X2x and its dual X2x*. Decomposition and reconstruction algorithms are derived from the construction.
Thu, 01 Jan 1998 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030541998-01-01T00:00:00Z
- Resolution enhancement for video clips: Tight frame approachhttps://scholarbank.nus.edu.sg/handle/10635/116775Title: Resolution enhancement for video clips: Tight frame approach
Authors: Chan, R.H.; Shen, Z.; Xia, T.
Abstract: Video clip consists of frames, and each frame can be considered as a transformed picture of the reference frame. In this paper, we briefly discuss a framelet method for high-resolution image reconstruction to enhance the resolution of video clips. The detailed discussion can be found in [10]. Experiments on an actual video clip show that our method can provide information that are not discernable from the given video clip. © 2005 IEEE.
Sat, 01 Jan 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1167752005-01-01T00:00:00Z
- Minimal degrees recursive in 1-generic degreeshttps://scholarbank.nus.edu.sg/handle/10635/103549Title: Minimal degrees recursive in 1-generic degrees
Authors: Chong, C.T.; Downey, R.G.
Fri, 31 Aug 1990 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035491990-08-31T00:00:00Z
- Maximal chains in the turing degreeshttps://scholarbank.nus.edu.sg/handle/10635/103532Title: Maximal chains in the turing degrees
Authors: Chong, C.T.; Yu, L.
Abstract: We study the problem of existence of maximal chains in the Turing degrees. We show that: 1. ZF+DC+ "There exists no maximal chain in the Turing degrees" is equiconsistent with ZFC+" There exists an inaccessible cardinal"; 2. For all α ∈ 2ω,(ω1) L[α] = ω1 if and only if there exists a ∏1 I[a] maximal chain in the Turing degrees. As a corollary, ZFC + "There exists an inaccessible cardinal" is equiconsistent with ZFC + "There is no (bold face) ∏|1 1 maximal chain of Turing degrees". © 2007. Association for Symbolic Logic.
Sat, 01 Dec 2007 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035322007-12-01T00:00:00Z
- Linear independence of pseudo-splineshttps://scholarbank.nus.edu.sg/handle/10635/103495Title: Linear independence of pseudo-splines
Authors: Dong, B.; Shen, Z.
Abstract: In this paper, we show that the shifts of a pseudo-spline are linearly independent. This is stronger than the (more obvious) statement that the shifts of a pseudo-spline form a Riesz system. In fact, the linear independence of a compactly supported (refinable) function and its shifts has been studied in several areas of approximation and wavelet theory. Furthermore, the linear independence of the shifts of a pseudo-spline is a necessary and sufficient condition for the existence of a compactly supported function whose shifts form a biorthogonal dual system of the shifts of the pseudo-spline. © 2006 American Mathematical Society.
Fri, 01 Sep 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034952006-09-01T00:00:00Z
- Image deconvolution using a characterization of sharp images in wavelet domainhttps://scholarbank.nus.edu.sg/handle/10635/103395Title: Image deconvolution using a characterization of sharp images in wavelet domain
Authors: Ji, H.; Li, J.; Shen, Z.; Wang, K.
Abstract: Image deconvolution is a challenging ill-posed problem when only partial information of the blur kernel is available. Certain regularization on sharp images has to be imposed to constrain the estimation of true images during the blind deconvolution process. Based on the observation that an image of sharp edges tends to minimize the ratio between the l 1 norm and the l 2 norm of its wavelet frame coefficients, we propose a new characterization of sharp images for image deconvolution. A two-stage method is then developed to solve semi-blind image deconvolution problems. The proposed method is fast, easy to implement and does not require rigorous parameter tune-up. Such a regularization can also be applied to solve non-blind image deconvolution problems and the resulting algorithm achieves good performance without rigorous parameter tune-up. © 2011 Elsevier Inc. All rights reserved.
Thu, 01 Mar 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033952012-03-01T00:00:00Z
- Multidimensional interpolatory subdivision schemeshttps://scholarbank.nus.edu.sg/handle/10635/103574Title: Multidimensional interpolatory subdivision schemes
Authors: Riemenschneider, S.D.; Shen, Z.
Abstract: This paper presents a general construction of multidimensional interpolatory subdivision schemes. In particular, we provide a concrete method for the construction of bivariate interpolatory subdivision schemes of increasing smoothness by finding an appropriate mask to convolve with the mask of a three-direction box spline Br,r,r of equal multiplicities. The resulting mask for the interpolatory subdivision exhibits all the symmetries of the three-direction box spline and with this increased symmetry comes increased smoothness. Several examples are computed (for r = 2, . . . , 8). Regularity criteria in terms of the refinement mask are establíshed and applied to the examples to estimate their smoothness.
Wed, 01 Jan 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035741997-01-01T00:00:00Z
- Positive Reducibility of the Interior of Filled Julia Setshttps://scholarbank.nus.edu.sg/handle/10635/103950Title: Positive Reducibility of the Interior of Filled Julia Sets
Authors: Chong, C.T.
Thu, 01 Dec 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039501994-12-01T00:00:00Z
- On existence and weak stability of matrix refinable functionshttps://scholarbank.nus.edu.sg/handle/10635/103705Title: On existence and weak stability of matrix refinable functions
Authors: Jiang, Q.; Shen, Z.
Abstract: We consider the existence of distributional (or L2) solutions of the matrix refinement equation Φ̂ = P(·/2)Φ̂(·/2), where P is an r × r matrix with trigonometric polynomial entries. One of the main results of this paper is that the above matrix refinement equation has a compactly supported distributional solution if and only if the matrix P(0) has an eigenvalue of the form 2n, n ∈ ℤ+. A characterization of the existence of L2-solutions of the above matrix refinement equation in terms of the mask is also given. A concept of L2-weak stability of a (finite) sequence of function vectors is introduced. In the case when the function vectors are solutions of a matrix refinement equation, we characterize this weak stability in terms of the mask.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1037051999-01-01T00:00:00Z
- Dual wavelet frames and riesz bases in sobolev spaceshttps://scholarbank.nus.edu.sg/handle/10635/103163Title: Dual wavelet frames and riesz bases in sobolev spaces
Authors: Han, B.; Shen, Z.
Abstract: This paper generalizes the mixed extension principle in L 2(ℝd ) of (Ron and Shen in J. Fourier Anal. Appl. 3:617-637, 1997) to a pair of dual Sobolev spaces H s (ℝd ) and H -s (ℝ d ). In terms of masks for φ,ψ; 1,ψ; L H s (ℝd ) and φ, tildeψ}1},ldots,tildeψ}L}in H-s}({R{d , simple sufficient conditions are given to ensure that (X s (φψ; 1,ψ; L ), X-s}(tildeφ};tildeψ}1}, ldots,tildeψ}L})) forms a pair of dual wavelet frames in (H s ( d ),H -s ( d )), where begin{array}{ll}Xs} bigl(phi;psi1},ldots,psiL}bigr):=&biglφ(cdot-k):kin {Z{d}bigr [9pt]&{}cupbigl{2j(d/2-s)}ψ;}(2j}cdot-k):jin {N}}-{0}, kin{Z{d},ell=1,ldots,Lbigr}.end{array} For s>0, the key of this general mixed extension principle is the regularity of φ, ψ; 1,ψ; L , and the vanishing moments of tildeψ}1},ldots,tildeψ}L} , while allowing tildeφ} , tildeψ}1},ldots,tildeψ}L} to be tempered distributions not in L 2( d ) and ψ; 1,ψ; L to have no vanishing moments. So, the systems X s (φψ; 1,ψ; L ) and X-s}(tildeφ};tildeψ}1},ldots,tildeψ}L may not be able to be normalized into a frame of L 2( d ). As an example, we show that {2 j(1/2-s) B m (2 j ?-k):j ? 0,k ?} is a wavelet frame in H s () for any 0
Mon, 01 Jun 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031632009-06-01T00:00:00Z
- Distributional solutions of nonhomogeneous discrete and continuous refinement equationshttps://scholarbank.nus.edu.sg/handle/10635/103149Title: Distributional solutions of nonhomogeneous discrete and continuous refinement equations
Authors: Rong-Qing, J.; Jiang, Q.; Shen, Z.
Abstract: Discrete and continuous refinement equations have been widely studied in the literature for the last few years, due to their applications to the areas of wavelet analysis and geometric modeling. However, there is no "universal" theorem that deals with the problem about the existence of compactly supported distributional solutions for both discrete and continuous refinement equations simultaneously. In this paper, we provide a uniform treatment for both equations. In particular, a complete characterization of the existence of distributional solutions of nonhomogeneous discrete and continuous refinement equations is given, which covers all cases of interest. © 2000 Society for Industrial and Applied Mathematics.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1031492000-01-01T00:00:00Z
- Construction of compactly supported biorthogonal waveletshttps://scholarbank.nus.edu.sg/handle/10635/103051Title: Construction of compactly supported biorthogonal wavelets
Authors: Riemenschneider, S.D.; Shen, Z.
Abstract: This paper presents a construction of compactly supported dual functions of a given box spline in L 2(ℝ s). In particular, a concrete method for the construction of compactly supported dual functions of bivariate box splines of increasing smoothness is provided.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030511999-01-01T00:00:00Z
- On the role of the collection principle for ∑2 0 -formulas in second-order reverse mathematicshttps://scholarbank.nus.edu.sg/handle/10635/103836Title: On the role of the collection principle for ∑2 0 -formulas in second-order reverse mathematics
Authors: Chong, C.T.; Lempp, S.; Yang, Y.
Abstract: We show that the principle PART from Hirschfeldt and Shore is equivalent to the ∑2 0 -Bounding principle B∑2 0 over RCA0, answering one of their open questions. Furthermore, we also fill a gap in a proof of Cholak, Jockusch and Slaman by showing that D2 2 implies B∑2 0 and is thus indeed equivalent to Stable Ramsey's Theorem for Pairs (SRT2 2 ). This also allows us to conclude that the combinatorial principles IPT 2 2 , SPT2 2 and SIPT2 2 defined by Dzhafarov and Hirst all imply B∑2 0 and thus that SPT2 2 and SIPT2 2 are both equivalent to SRT2 2 as well. Our proof uses the notion of a bi-tame cut, the existence of which we show to be equivalent, over RCA0, to the failure of B∑2 0 © 2009 American Mathematical Society.
Mon, 01 Mar 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1038362010-03-01T00:00:00Z
- Frame based segmentation for medical imageshttps://scholarbank.nus.edu.sg/handle/10635/103295Title: Frame based segmentation for medical images
Authors: Dong, B.; Chien, A.; Shen, Z.
Abstract: Medical image segmentation is an important but difficult problem that attracts tremendous attention from researchers in various fields. In this paper, we propose a frame based model, as well as a fast implementation, for general medical image segmentation problems. Our model combines ideas of the frame based image restoration model of [J. Cai, S. Osher, and Z. Shen, Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 8(2), 337-369, 2009] with ideas of the total variation based segmentation model of [T. Chan and L. Vese, Scale-Space Theories in Computer Vision, 141-151, 1999], [T. Chan and L. Vese, IEEE Transactions on image processing, 10(2), 266-277, 2001], [T. Chan, S. Esedoglu and M. Nikolova, ALGORITHMS, 66(5), 1632-1648], and [X. Bresson, S. Esedoglu, P. Vandergheynst, J. Thiran and S. Osher, Journal of Mathematical Imaging and Vision, 28(2), 151-167, 2007]. Numerical experiments show that the proposed frame based model outperforms the total variation based model in terms of capturing key features of biological structures. Successful segmentations of blood vessels and aneurysms in 3D CT angiography images are also presented. © 2011 International Press.
Wed, 01 Jun 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1032952011-06-01T00:00:00Z
- Constructions of sequences with almost perfect linear complexity profile from curves over finite fieldshttps://scholarbank.nus.edu.sg/handle/10635/43016Title: Constructions of sequences with almost perfect linear complexity profile from curves over finite fields
Authors: Xing, C.; Niederreiter, H.; Lam, K.Y.; Ding, C.
Abstract: Sequences with almost perfect linear complexity profile are of importance for the linear complexity theory of sequences. In this paper we present several constructions of sequences with almost perfect linear complexity profile based on algebraic curves over finite fields. Moreover, some interesting consequences and examples are derived from our constructions. © 1999 Academic Press.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/430161999-01-01T00:00:00Z
- Some new codes from algebraic curveshttps://scholarbank.nus.edu.sg/handle/10635/43015Title: Some new codes from algebraic curves
Authors: Ding, C.; Niederreiter, H.; Xing, C.
Abstract: Based on a construction of Xing, Niederreiter, and Lam [7], some new linear codes are found from suitable algebraic curves over finite fields. These codes have better parameters compared with Brouwer's table [1]. © 2000 IEEE.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/430152000-01-01T00:00:00Z
- Secret-sharing with a class of ternary codeshttps://scholarbank.nus.edu.sg/handle/10635/43020Title: Secret-sharing with a class of ternary codes
Authors: Ding, C.; Kohel, D.R.; Ling, S.
Abstract: Secret-sharing is an important topic of cryptography and has applications in information security. One approach to the construction of secret-sharing schemes is based on error-correcting codes. In this paper, we describe a secret-sharing scheme based on a class of ternary codes (Ding et al. IEEE Trans. Inform. Theory IT-46 (2000) 280-284). We determine the access structure and prove properties of the secret-sharing scheme. © 2000 Elsevier Science B.V. All rights reserved.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/430202000-01-01T00:00:00Z
- Construction and enumeration of all binary duadic codes of length pmhttps://scholarbank.nus.edu.sg/handle/10635/43014Title: Construction and enumeration of all binary duadic codes of length pm
Authors: Ding, C.; Lam, K.Y.; Xing, C.
Abstract: In this paper we present a binary-tree approach to the construction of all binary duadic codes of length n = pm. We also calculate the number of binary duadic codes of length n = pm, where p = ± 1 (mod 8) is a prime.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/430141999-01-01T00:00:00Z
- Some new codes from algebraic curveshttps://scholarbank.nus.edu.sg/handle/10635/43017Title: Some new codes from algebraic curves
Authors: Ding, Cunsheng; Niederreiter, Harald; Xing, Chaoping
Abstract: Based on a construction of Xing, Niederreiter, and Lam, some new linear codes are found from suitable algebraic curves over finite fields. These codes have better parameters compared with Brouwer's table.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/430172000-01-01T00:00:00Z
- Supersymmetric AdS 5 black holes and strings from 5D N= 4 gauged supergravityhttps://scholarbank.nus.edu.sg/handle/10635/210796Title: Supersymmetric AdS 5 black holes and strings from 5D N= 4 gauged supergravity
Authors: Dao, H.L.; Karndumri, P.
Abstract: We study supersymmetric AdS 3 × Σ 2 and AdS 2 × Σ 3 solutions, with Σ 2 = S 2 , H 2 and Σ 3 = S 3 , H 3 , in five-dimensional N= 4 gauged supergravity coupled to five vector multiplets. The gauge groups considered here are U(1) × SU(2) × SU(2) , U(1) × SO(3 , 1) and U(1) × SL(3 , R). For U(1) × SU(2) × SU(2) gauge group admitting two supersymmetric N= 4 AdS 5 vacua, we identify a new class of AdS 3 × Σ 2 and AdS 2 × H 3 solutions preserving four supercharges. Holographic RG flows describing twisted compactifications of N= 2 four-dimensional SCFTs dual to the AdS 5 vacua to the SCFTs in two and one dimensions dual to these geometries are numerically given. The solutions can also be interpreted as supersymmetric black strings and black holes in asymptotically AdS 5 spaces with near horizon geometries given by AdS 3 × Σ 2 and AdS 2 × H 3 , respectively. These solutions broaden previously known black brane solutions including half-supersymmetric AdS 5 black strings recently found in N= 4 gauged supergravity. Similar solutions are also studied in non-compact gauge groups U(1) × SO(3 , 1) and U(1) × SL(3 , R). © 2019, The Author(s).
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2107962019-01-01T00:00:00Z
- Characterization of compactly supported refinable splineshttps://scholarbank.nus.edu.sg/handle/10635/111150Title: Characterization of compactly supported refinable splines
Authors: Lawton, W.; Lee, S.L.; Shen, Z.
Abstract: We prove that a compactly supported spline function φ of degree k satisfies the scaling equation {Mathematical expression} for some integer m ≥ 2, if and only if {Mathematical expression} where p(n) are the coefficients of a polynomial P(z) such that the roots of P(z)(z - 1)k+1 TM are mapped into themselves by the mapping z →zm, and Bk is the uniform B-spline of degree k. Furthermore, the shifts of φ form a Riesz basis if and only if P is a monomial. © 1995 J.C. Baltzer AG, Science Publishers.
Sun, 01 Jan 1995 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1111501995-01-01T00:00:00Z
- Holographic RG flows and AdS 5 black strings from 5D half-maximal gauged supergravityhttps://scholarbank.nus.edu.sg/handle/10635/212484Title: Holographic RG flows and AdS 5 black strings from 5D half-maximal gauged supergravity
Authors: Dao, H.L.; Karndumri, P.
Abstract: We study five-dimensional N= 4 gauged supergravity coupled to five vector multiplets with compact and non-compact gauge groups U(1) × SU(2) × SU(2) and U(1) × SO(3 , 1). For U(1) × SU(2) × SU(2) gauge group, we identify N= 4 AdS 5 vacua with U(1) × SU(2) × SU(2) and U(1) × SU(2) diag symmetries and analytically construct the corresponding holographic RG flow interpolating between these critical points. The flow describes a deformation of the dual N= 2 SCFT driven by vacuum expectation values of dimension-two operators. In addition, we study AdS 3 × ? 2 geometries, for ? 2 being a two-sphere S 2 or a two-dimensional hyperbolic space H 2 , dual to twisted compactifications of N= 2 SCFTs with flavor symmetry SU(2). We find a number of AdS 3 × H 2 solutions preserving eight supercharges for different twists from U(1) × U(1) × U(1) and U(1) × U(1) diag gauge fields. We numerically construct various RG flow solutions interpolating between N= 4 AdS 5 critical points and these AdS 3 × H 2 geometries in the IR. The solutions can also be interpreted as supersymmetric black strings in asymptotically AdS 5 space. These types of holographic solutions are also studied in non-compact U(1) × SO(3 , 1) gauge group. In this case, only one N= 4 AdS 5 vacuum exists, and we give an RG flow solution from this AdS 5 to a singular geometry in the IR corresponding to an N= 2 non-conformal field theory. An AdS 3 × H 2 solution together with an RG flow between this vacuum and the N= 4 AdS 5 are also given. © 2019, The Author(s).
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2124842019-01-01T00:00:00Z
- On the linear complexity profile of some new explicit inversive pseudorandom numbershttps://scholarbank.nus.edu.sg/handle/10635/132768Title: On the linear complexity profile of some new explicit inversive pseudorandom numbers
Authors: Meidl, W.; Winterhof, A.
Abstract: Linear complexity and linear complexity profile are interesting characteristics of a sequence for applications in cryptography and Monte-Carlo methods. We introduce some new explicit inversive pseudorandom number generators and prove lower bounds on their linear complexity profile which are close to the best possible. © 2003 Elsevier Inc. All rights reserved.
Thu, 01 Apr 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1327682004-04-01T00:00:00Z
- On the autocorrelation of cyclotomic generatorshttps://scholarbank.nus.edu.sg/handle/10635/132769Title: On the autocorrelation of cyclotomic generators
Authors: Meidl, W.; Winterhof, A.
Abstract: We extend a result of Ding and Helleseth on the autocorrelation of a cyclotomic generator in several ways. We define and analyze cyclotomic generators of arbitrary orders and over arbitrary finite fields, and we consider two, in general, different definitions of autocorrelation. Cyclotomic generators are closely related to the discrete logarithm. Hence, the results of this paper do not only describe interesting cryptographic properties of cyclotomic generators and their generalizations but also desirable features of the discrete logarithm. © Springer-Verlag Berlin Heidelberg 2004.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1327692004-01-01T00:00:00Z
- Exponential and laplace approximation for occupation statistics of branching random walkhttps://scholarbank.nus.edu.sg/handle/10635/197817Title: Exponential and laplace approximation for occupation statistics of branching random walk
Authors: Peköz, E.A.; Röllin, A.; Ross, N.
Abstract: We study occupancy counts for the critical nearest-neighbor branching random walk on the d-dimensional lattice, conditioned on non-extinction. For d 3, Lalley and Zheng [4] showed that the properly scaled joint distribution of the number of sites occupied by j generation-n particles, j = 1, 2, …, converges in distribution as n goes to infinity, to a deterministic multiple of a single exponential random variable. The limiting exponential variable can be understood as the classical Yaglom limit of the total population size of generation n. Here we study the second order fluctuations around this limit, first, by providing a rate of convergence in the Wasserstein metric that holds for all d 3, and second, by showing that for d 7, the weak limit of the scaled joint differences between the number of occupancy-j sites and appropriate multiples of the total population size converge in the Wasserstein metric to a multivariate symmetric Laplace distribution. We also provide a rate of convergence for this latter result. © 2020, Institute of Mathematical Statistics. All rights reserved.
Wed, 01 Jan 2020 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1978172020-01-01T00:00:00Z
- dS5 vacua from matter-coupled 5D N= 4 gauged supergravityhttps://scholarbank.nus.edu.sg/handle/10635/209552Title: dS5 vacua from matter-coupled 5D N= 4 gauged supergravity
Authors: Dao, H.L.; Karndumri, P.
Abstract: We study dS5 vacua within matter-coupled N= 4 gauged supergravity in five dimensions using the embedding tensor formalism. With a simple ansatz for solving the extremization and positivity of the scalar potential, we derive a set of conditions for the gauged supergravity to admit dS5 as maximally symmetric background solutions. The results provide a new approach for finding dS5 vacua in five-dimensional N= 4 gauged supergravity and explain a number of notable features pointed out in previous works. These conditions also determine the form of the gauge groups to be SO(1 , 1) × Gnc with Gnc being a non-abelian non-compact group. In general, Gnc can be a product of SO(1, 2) and a smaller non-compact group G?nc together with (possibly) a compact group. The SO(1, 1) factor is gauged by one of the six graviphotons, that is singlet under SO(5) ? USp(4) R-symmetry. The compact parts of SO(1, 2) and G?nc are gauged by vector fields from the gravity and vector multiplets, respectively. In addition, we explicitly study dS5 vacua for a number of gauge groups and compute scalar masses at the vacua. As in the four-dimensional N= 4 gauged supergravity, all the dS5 vacua identified here are unstable. © 2019, The Author(s).
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2095522019-01-01T00:00:00Z
- Higher-order fluctuations in dense random graph modelshttps://scholarbank.nus.edu.sg/handle/10635/233250Title: Higher-order fluctuations in dense random graph models
Authors: Kaur, Gursharn; Roellin, A.
Abstract: Our main results are quantitative bounds in the multivariate normal approximation of centred subgraph counts in random graphs generated by a general graphon and independent vertex labels. We are interested in these statistics because they are key to understanding fluctuations of regular subgraph counts — a cornerstone of dense graph limit theory. We also identify the resulting limiting Gaussian stochastic measures by means of the theory of generalised U-statistics and Gaussian Hilbert spaces, which we think is a suitable framework to describe and understand higher-order fluctuations in dense random graph models. With this article, we believe we answer the question “What is the central limit theorem of dense graph limit theory?”. We complement the theory with some statistical applications to illustrate the use of centred subgraph counts in network modelling. © 2021, Institute of Mathematical Statistics. All rights reserved.
Fri, 01 Jan 2021 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2332502021-01-01T00:00:00Z
- Cosmological solutions from 4d n=4 matter-coupled supergravityhttps://scholarbank.nus.edu.sg/handle/10635/233251Title: Cosmological solutions from 4d n=4 matter-coupled supergravity
Authors: Dao, H. L.
Abstract: From four-dimensional N = 4 matter-coupled gauged supergravity, we study smooth time-dependent cosmological solutions interpolating between a dS2 × ?2 spacetime, with ?2 = S2 and H2, in the infinite past and a dS4 spacetime in the infinite future. The solutions were obtained by solving the second-order equations of motion from all the ten gauged theories known to admit dS4 solutions, of which there are two types. Type I dS gauged theories can admit both dS solutions as well as supersymmetric AdS solutions while type II dS gauged theories only admit dS solutions. We also study the extent to which the first-order equations that solve the aforementioned second-order field equations fail to admit the dS4 vacua and their associated cosmological solutions. © 2021 The Author(s). Published by IOP Publishing Ltd.
Fri, 01 Oct 2021 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2332512021-10-01T00:00:00Z
- Simultaneous spatiotemporal super-resolution and multi-parametric fluorescence microscopyhttps://scholarbank.nus.edu.sg/handle/10635/233071Title: Simultaneous spatiotemporal super-resolution and multi-parametric fluorescence microscopy
Authors: Sankaran, Jagadish; Balasubramanian, Harikrushnan; Tang, Wai Hoh; Ng, Xue Wen; Röllin, Adrian; Wohland, Thorsten
Abstract: Super-resolution microscopy and single molecule fluorescence spectroscopy require mutually exclusive experimental strategies optimizing either temporal or spatial resolution. To achieve both, we implement a GPU-supported, camera-based measurement strategy that highly resolves spatial structures (~100 nm), temporal dynamics (~2 ms), and molecular brightness from the exact same data set. Simultaneous super-resolution of spatial and temporal details leads to an improved precision in estimating the diffusion coefficient of the actin binding polypeptide Lifeact and corrects structural artefacts. Multi-parametric analysis of epidermal growth factor receptor (EGFR) and Lifeact suggests that the domain partitioning of EGFR is primarily determined by EGFR-membrane interactions, possibly sub-resolution clustering and inter-EGFR interactions but is largely independent of EGFR-actin interactions. These results demonstrate that pixel-wise cross-correlation of parameters obtained from different techniques on the same data set enables robust physicochemical parameter estimation and provides biological knowledge that cannot be obtained from sequential measurements. © 2021, The Author(s).
Fri, 19 Mar 2021 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2330712021-03-19T00:00:00Z
- dS4 vacua from matter-coupled 4D N= 4 gauged supergravityhttps://scholarbank.nus.edu.sg/handle/10635/211876Title: dS4 vacua from matter-coupled 4D N= 4 gauged supergravity
Authors: Dao, H.L.; Karndumri, P.
Abstract: We study dS4 vacua within matter-coupled N= 4 gauged supergravity in the embedding tensor formalism. We derive a set of conditions for the existence of dS4 solutions by using a simple ansatz for solving the extremization and positivity of the scalar potential. We find two classes of gauge groups that lead to dS4 vacua. One of them consists of gauge groups of the form Ge× Gm× H with H being a compact group and Ge× Gm a non-compact group with SO(3) × SO(3) subgroup and dyonically gauged. These gauge groups are the same as those giving rise to maximally supersymmetric AdS4 vacua. The dS4 and AdS4 vacua arise from different coupling ratios between Ge and Gm factors. Another class of gauge groups is given by SO(2,1)e×SO(2,1)m×Gnc×Gnc?×H with SO(2, 1), Gnc and Gnc? dyonically gauged. We explicitly check that all known dS4 vacua in N= 4 gauged supergravity satisfy the aforementioned conditions, hence the two classes of gauge groups can accommodate all the previous results on dS4 vacua in a simple framework. Accordingly, the results provide a new approach for finding dS4 vacua. In addition, relations between the embedding tensors for gauge groups admitting dS4 and dS5 vacua are studied, and a new gauge group, SO(2 , 1) × SO(4 , 1) , with a dS4 vacuum is found by applying these relations to SO(1 , 1) × SO(4 , 1) gauge group in five dimensions. © 2019, The Author(s).
Tue, 01 Jan 2019 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2118762019-01-01T00:00:00Z
- Stability and orthonormality of multivariate refinable functionshttps://scholarbank.nus.edu.sg/handle/10635/111211Title: Stability and orthonormality of multivariate refinable functions
Authors: Lawton, W.; Lee, S.L.; Shen, Z.
Abstract: This paper characterizes the stability and orthonormality of the shifts of a multidimensional (M, c) refinable function φ in terms of the eigenvalues and eigenvectors of the transition operator Wcau defined by the autocorrelation cau of its refinement mask c, where M is an arbitrary dilation matrix. Another consequence is that if the shifts of φ form a Riesz basis, then Wcau has a unique eigenvector of eigenvalue 1, and all of its other eigenvalues lie inside the unit circle. The general theory is applied to two-dimensional nonseparable (M, c) refinable functions whose masks are constructed from Daubechies' conjugate quadrature filters.
Tue, 01 Jul 1997 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1112111997-07-01T00:00:00Z
- Respondent-driven sampling and sparse graph convergencehttps://scholarbank.nus.edu.sg/handle/10635/214066Title: Respondent-driven sampling and sparse graph convergence
Authors: Athreya, S.; Roellin, A.
Abstract: We consider a particular respondent-driven sampling procedure governed by a graphon. Using a specific clumping procedure of the sampled vertices, we construct a sequence of sparse graphs. If the sequence of the vertex-sets is stationary, then the sequence of sparse graphs converges to the governing graphon in the cut-metric. The tools used are a concentration inequality for Markov chains and the Stein-Chen method. © 2018, University of Washington. All rights reserved.
Mon, 01 Jan 2018 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/2140662018-01-01T00:00:00Z
- Local limit theorems via Landau-Kolmogorov inequalitieshttps://scholarbank.nus.edu.sg/handle/10635/127236Title: Local limit theorems via Landau-Kolmogorov inequalities
Authors: Roellin, Adrian; Ross, Nathan
Thu, 01 Jan 2015 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1272362015-01-01T00:00:00Z
- Duadic sequences of prime lengthshttps://scholarbank.nus.edu.sg/handle/10635/38915Title: Duadic sequences of prime lengths
Authors: Ding, C.; Helleseth, T.; Lam, K.Y.
Abstract: Legendre sequences have a number of interesting properties. Their counterparts in coding theory are binary quadratic residue codes. In this paper we study a class of binary sequences, called duadic sequences whose counterparts in coding theory are duadic codes. We calculate their linear complexity, study their autocorrelation and crosscorrelation properties, give exact formulas for the number of bigrams in a cycle, investigate their decimation properties, and discuss their implementation. © 2000 Elsevier Science B.V. All rights reserved.
Sat, 01 Jan 2000 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/389152000-01-01T00:00:00Z
- Restoring chopped and nodded images by tight frameshttps://scholarbank.nus.edu.sg/handle/10635/104621Title: Restoring chopped and nodded images by tight frames
Authors: Chan, R.; Shen, L.; Shen, Z.
Abstract: In infrared astronomy, the observed chopped and nodded image g can be viewed as the image obtained by passing the true image f through a highpass filter. Here we propose an iterative restoration algorithm by building up a tight frame wavelet system from a multiresolution analysis that has the highpass filter as one of the wavelet filters. To recover f, the low frequency information of f hidden in g is unfolded by a wavelet decomposition and reconstruction algorithm and combined with the given high frequency information in g. The main advantage of using our method to restore chopped and nodded images is that there are fewer artifacts as compared to the well-known projected Landweber method. Also the noise in the restored image is significantly reduced. Simulated and real images are tested to illustrate the efficiency of our method. Here, we briefly describe the main ideas of our recent paper1 and the details can be found there.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1046212003-01-01T00:00:00Z
- A three-parameter binomial approximationhttps://scholarbank.nus.edu.sg/handle/10635/129682Title: A three-parameter binomial approximation
Authors: Peköz, E.A.; Shwartz, M.; Röllin, A.; Čekanavičius, V.
Abstract: We approximate the distribution of the sum of independent but not necessarily identically distributed Bernoulli random variables using a shifted binomial distribution, where the three parameters (the number of trials, the probability of success, and the shift amount) are chosen to match the first three moments of the two distributions. We give a bound on the approximation error in terms of the total variation metric using Stein's method. A numerical study is discussed that shows shifted binomial approximations are typically more accurate than Poisson or standard binomial approximations. The application of the approximation to solving a problem arising in Bayesian hierarchical modeling is also discussed. © Applied Probability Trust 2009.
Tue, 01 Dec 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1296822009-12-01T00:00:00Z
- Hyperhypersimple sets and Δ2 systemshttps://scholarbank.nus.edu.sg/handle/10635/103392Title: Hyperhypersimple sets and Δ2 systems
Authors: Chong, C.T.
Mon, 09 Oct 1989 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1033921989-10-09T00:00:00Z
- A wavelet method for high-resolution image reconstruction with displacement errorshttps://scholarbank.nus.edu.sg/handle/10635/104527Title: A wavelet method for high-resolution image reconstruction with displacement errors
Authors: Chan, R.H.; Chan, T.F.; Shen, L.; Shen, Z.
Mon, 01 Jan 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1045272001-01-01T00:00:00Z
- Cyclotomy and duadic codes of prime lengthshttps://scholarbank.nus.edu.sg/handle/10635/38909Title: Cyclotomy and duadic codes of prime lengths
Authors: Ding, C.; Pless, V.
Abstract: In this paper we present a cyclotomic approach to the construction of all binary duadic codes of prime lengths. We calculate the number of all binary duadic codes for a given prime length and that of all duadic codes that are not quadratic residue codes. We give necessary and sufficient conditions for p such that all binary duadic codes of length p are quadratic residue (Q.R.) codes. We also show how to determine some weights of duadic codes with the help of cyclotomic numbers. © 1999 IEEE.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/389091999-01-01T00:00:00Z